4. For parts (a) (d), copy the number line below. Locate and label a point representing each fraction described.

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1 A C E Applications Connections Extensions Applications Investigation. Describe, in writing or with pictures, how compares to.. Multiple Choice On a number line from 0 to 0, where is located? A. between 0 and B. between and C. between and D. between and. Copy the number line below. Locate and label marks representing,, and 0.. For parts (a) (d), copy the number line below. Locate and label a point representing each fraction described. a. a fraction close to but greater than b. a fraction close to but less than c. a fraction close to but greater than d. a fraction close to but less than For Exercises, write each mixed number as an improper fraction..... For Exercises, write each improper fraction as a mixed number Comparing Bits and Pieces Investigation

2 . What numbers have an absolute value of?. What are some numbers that have an absolute value greater than?. A football team has four chances with the ball to gain ten yards and keep going to try to make a touchdown. A team gained yards, lost, gained, and lost. a. How many total yards did the team move (forward or backward)? b. Did they gain enough to keep the ball? Explain your reasoning. In many cold places, weather reports often include wind chills, the temperature of how cold it feels outside when you include the wind making it feel colder. For Exercises, write an inequality statement for the wind chills of the two locations.. Lincoln, NE compared to New Albin, IA F F. Viroqua, WI compared to Toledo, OH F F. Minneapolis, MN compared to Duluth, MN 0 F F. Bozeman, MT compared to Rapid City, SD F F Comparing Bits and Pieces Investigation

3 0. Mr. Bergman is having an end-of-the-year trivia contest. Each correct answer is worth 00 points, and each incorrect answer is worth 0 points. At the end of the contest Mr. Bergman is surprised by the final scores. Blue Team Orange Team Purple Team 0 points 0 points 00 points The Blue team says they win because they have the highest score. The White team says that 0 is greater than 0, so they win. Which team should be called the winner? Explain.. Mrs. O Brien s students are playing The Ordering Game as a whole class. A student draws five cards numbered 0 to 0. She rearranges the cards in different ways, and the class tries to figure out the reason for the order. In each of the orderings below, what reason was Ashley using for the order? Explain. Ashley draws these cards. a. Ordering # b. Ordering # c. Ordering # Comparing Bits and Pieces Investigation

4 . Use Ashley s three ordering methods from the previous problem to order the five cards that Herbert drew. Is there another ordering you could do that Ashley didn t show? Explain. Herbert s Cards:. Franklin Middle School is having an end-of-the-year carnival with different games. One of the games is a bean-bag toss. The object is to get zero, or as close to zero as possible on the toss. Joseph s bag lands on an area labeled. Jeremiah s bag lands on an area labeled. Joseph says, I win because <. Jeremiah says, No, we have to decide whose score is closer to zero. Since and, my score is closer to zero. I win. Who is correct? Explain.. The elevation of different places on Earth is often given as the height above sea level, rounded to the nearest foot. Likewise, there are many places in the world whose elevation is below sea level. These are useful measurements because sea level is relatively constant across the planet. City Indio, California Denver, Colorado Wenzuan, China New Orleans, LA Death Valley, California Height above Sea Level 0 feet,0 feet,00 feet feet 00 feet a. Order the cities in the table from lowest elevation to highest elevation. b. Order the cities from least to greatest distance from sea level. c. Did you use absolute value in either part (a) or (b)? Explain. Comparing Bits and Pieces Investigation

5 As Rosemary works through some homework problems, she notices that negative numbers can often be rewritten using positive numbers if you change what you are talking about. For example, a golf score was given as but Rosemary rewrote this as shots under par. For Exercises, rewrite each negative situation using a positive value.. A savings account balance is $.00.. The elevation of a city is 0 feet.. A quarterback ran for yards.. The amount of money a lemonade stand made on a rainy day was $0.00. For Exercises 0, compare each pair of fractions using benchmarks, number lines, and other strategies. Then use a less than (<), greater than (>), or equal to (=) symbol to complete each number sentence For Exercises, find a rational number between each pair of numbers.. and. and. and. and For Exercises 0, between which two benchmarks (of 0,,,, and ) does each fraction fall? Tell which is the nearer benchmark Comparing Bits and Pieces Investigation

6 . Multiple Choice Which fraction is greatest? F. G. H. J.. Multiple Choice Find the opposite of each number below. Which one is greatest? A. B. C. D. A pan of lasagna cut into 00 servings is equally shared among a group of people. For Exercises, determine the portion of the pan that each person receives given the number of people in each group. Write your answer as both a fractional and a decimal part of a pan.. 0 people. 0 people. 0 people For Exercises, write a fraction equivalent to the decimal For Exercises 0, write a decimal equivalent to the fraction Which is greater, forty-five hundredths or six tenths? Explain. Draw a picture if it helps you explain.. Which is greater, 0. or 0.0? Explain. Draw a picture if it helps you explain. Comparing Bits and Pieces Investigation

7 For Exercises, a full one-hundredths grid represents the number. What fraction and decimal is represented by each of the shaded parts?.... Name three fractions whose decimal equivalent is 0.0. Explain how you know each fraction is equivalent to 0.0. Draw a picture if it helps you explain. For Exercises 0, copy the part of the number line given. Then find the step by determining the difference from one mark to another. Label the unlabeled marks with decimal numbers. Sample: The step is Comparing Bits and Pieces Investigation

8 For Exercises, give the fraction listed that is nearest on the number line to that decimal For Exercises, copy each pair of numbers. Insert <, >, or = to make a true statement For Exercises and, rewrite the numbers in order from least to greatest.. 0., 0., 0., 0., 0., 0, 0.00, Multiple Choice The orchestra at Johnson School is responsible for cleaning up a -mile section of highway. There are students in the orchestra. If each orchestra member cleans the same-size section, which of the decimals indicates the part of a mile cleaned by each student? F. 0. G. 0. H. 0. J. 0. Comparing Bits and Pieces Investigation

9 . Pilar divided by on her calculator and found that was approximately 0.. Find decimal approximations for each of the following fractions. a. b. e. Describe any patterns that you see. c. d.. Belinda used her calculator to find the decimal equivalent of the fraction. When she entered, the calculator gave an answer that looked familiar. Why do you think she recognized it?. Suppose a new student starts school today and your teacher asks you to teach her how to find decimal equivalents for fractions. What would you tell her? How would you convince the student that your method works? Connections For Exercises, use the following information. Each student activity group at Johnson School agreed to pick up litter along a ten-mile stretch of highway. Draw number lines to show your reasoning.. Kelly and Sean work together to clean a section of highway that is 0 miles long. Write this distance as a mixed number. 0. The Drama Club s stretch of highway is very hilly and full of trash. They can clean miles each day. Jacqueline says that in four days, they will be able to clean miles. Is she correct? Explain.. The Chess Club is cleaning a very littered section of highway. Each day the members clean miles of highway. After four days of hard work, Lakeisha says they have cleaned miles of highway. Glenda says they have cleaned miles of roadway. Who is right? Why? Comparing Bits and Pieces Investigation

10 . Ten students went to a pizza parlor together. They ordered eight small pizzas. a. How much pizza will each student get if they share the pizzas equally? Express your answer as a fraction and as a decimal. b. Explain how you thought about the problem. Draw a picture that would convince someone that your answer is correct.. If you look through a microscope that makes objects appear ten times larger, centimeter (cm) on a metric ruler looks like this: a. Copy this microscope s view of cm. Divide the length for cm into ten equal parts. What fraction of the centimeter does each of these parts represent? b. Now think about dividing one of these smaller parts into ten equal parts. What part of the original centimeter does each of the new segments represent? c. If you were to divide one of these new small parts into ten parts again, what part of the original centimeter would each of the new small parts represent? Comparing Bits and Pieces Investigation 0

11 Extensions For Exercises, find every fraction with a denominator less than 0 that is equivalent to the given fraction..... Find five fractions between. Does, reasoning., or and 0. represent the greatest part of a whole? Explain your. Copy the number line below. Place and label marks for 0,,, and. For Exercises 00 0, find an estimate if you cannot find an exact answer. You may find that drawing a number line, a hundredths grid, or some other diagram is useful in solving the problem. Explain your reasoning for each problem. 00. What is of? 0. What is 0. What is of? 0. What is 0. What is of? 0. What is of? of? of? Comparing Bits and Pieces Investigation